1 [/==============================================================================
2 Copyright (C) 2001-2015 Joel de Guzman
3 Copyright (C) 2001-2011 Hartmut Kaiser
5 Distributed under the Boost Software License, Version 1.0. (See accompanying
6 file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
7 ===============================================================================/]
8 [section Parsing Expression Grammar]
10 Parsing Expression Grammars (PEG) [footnote Bryan Ford: Parsing Expression
11 Grammars: A Recognition-Based Syntactic Foundation,
12 [@http://pdos.csail.mit.edu/~baford/packrat/popl04/]] are a derivative of
13 Extended Backus-Naur Form (EBNF) [footnote Richard E. Pattis: EBNF: A Notation
14 to Describe Syntax, [@http://www.cs.cmu.edu/~pattis/misc/ebnf.pdf]]
15 with a different interpretation, designed to represent a recursive descent
16 parser. A PEG can be directly represented as a recursive-descent parser.
18 Like EBNF, PEG is a formal grammar for describing a formal language in
19 terms of a set of rules used to recognize strings of this language.
20 Unlike EBNF, PEGs have an exact interpretation. There is only one valid
21 parse tree (see __ast__) for each PEG grammar.
25 Sequences are represented by juxtaposition like in EBNF:
29 The PEG expression above states that, in order for this to succeed,
30 `b` must follow `a`. Here's the syntax diagram:
34 Here's a trivial example:
38 which means the character `x` must be followed by a digit.
40 [note In __x3__, we use the `>>` for sequences since C++ does not
43 [heading Alternatives]
45 Alternatives are represented in PEG using the slash:
49 [note In __x3__, we use the `|` for alternatives just as in EBNF.]
51 Alternatives allow for choices. The expression above reads: try to match
52 `a`. If `a` succeeds, success, if not try to match `b`. This is a bit of
53 a deviation from the usual EBNF interpretation where you simply match
54 `a` *or* `b`. Here's the syntax diagram:
58 PEGs allow for ambiguity in the alternatives. In the expression above,
59 both `a` or `b` can both match an input string. However, only the first
60 matching alternative is valid. As noted, there can only be one valid
61 parse tree. [/FIXME: $$$ explain more about this $$$]
65 Again, like EBNF, PEG uses the regular-expression Kleene star and the
71 [note __x3__ uses the prefix star and plus since there is no postfix star or
74 Here are the syntax diagrams:
79 The first, called the Kleene star, matches zero or more of its subject
80 `a`. The second, plus, matches one ore more of its subject `a`.
82 Unlike EBNF, PEGs have greedy loops. It will match as much as it can
83 until its subject fails to match without regard to what follows. The following
84 is a classic example of a fairly common EBNF/regex expression failing to match
89 In PEG, alnum will eat as much alpha-numeric characters as it can
90 leaving nothing more left behind. Thus, the trailing digit will get
91 nothing. Loops are simply implemented in recursive descent code as for/while
92 loops making them extremely efficient. That is a definite advantage. On the
93 other hand, those who are familiar with EBNF and regex behavior might find the
94 behavior a major gotcha. PEG provides a couple of other mechanisms to circumvent
95 this. We will see more of these other mechanisms shortly.
99 In some cases, you may want to restrict a certain expression. You can think of a
100 PEG expression as a match for a potentially infinite set of strings. The
101 difference operator allows you to restrict this set:
105 The expression reads: match `a` but not `b`.